极限运算中的局部无穷小等价替换规则  

Equivalent Replacement Rules of Local Infinitesimal in Limit Mathematical Operation

作　　者：吴彬[1] 

机构地区：[1]南通职业大学基础课部,江苏南通226007

出　　处：《南通职业大学学报》2011年第4期78-80,共3页Journal of Nantong Vocational University

摘　　要：无穷小的等价替换是简化极限计算的有效途径之一,一般只适用于无穷小之比的计算。文章通过对无穷小和式中某一项无穷小进行等价替换后所得的新和式与原和式的比较分析,得出新和式与原和式能等价的充分必要条件;在此基础上进一步得到结论:只要和式中两项无穷小不是比值为-1的同阶无穷小,新和式与原和式必等价。这为无穷小之比极限计算中能否对分子或分母的和式中的单项无穷小实施等价替换来简化运算提供了一个判断依据。Equivalent replacement of infinitesimal is one of the efficient ways to simplify limit mathematical operation, which generally applies to calculate the infinitesimal ratio. Through the comparison and analysis of the original and new formula which is from the equivalent substitution of an infinitesimal in the infinitesimal formula, we can conclude necessary and sufficient conditions that the new formula is equivalent to the original one. Based on this, a further conclusion can be made that as long as the two infinitesimal items in the formula are not the same order infinitesimal with the ratio of -1, the new formula must be equivalent to the old one. Thus, it provides a judgment evidence for weather the individual infinitesimal can be replaced equivalently in the Numerator or denominator formula to simplify the calculation in limit mathematical operation.

关 键 词：等价无穷小 无穷小和式 等价替换 

分 类 号：O171[理学—数学]